Switzerland is not a member of the EU but have common procedures due to their bilaterals. Birds are listed as CITES or not CITES. According to the scientific name of the bird will be listed in either one.
If your bird is listed a CITES bird then you will be required to have a CITES import for Switzerland in order to enter. It is not recommended if the bird will not reside in Switzerland.
If the bird is listed as none CITES,
Regulations on importing pet birds